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 A326881 Number of set-systems with {} that are closed under intersection and cover n vertices. 13
 1, 1, 5, 71, 4223, 2725521, 151914530499, 28175294344381108057 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA Inverse binomial transform of A102895. - Andrew Howroyd, Aug 10 2019 EXAMPLE The a(2) = 5 set-systems:   {{},{1,2}}   {{},{1},{2}}   {{},{1},{1,2}}   {{},{2},{1,2}}   {{},{1},{2},{1,2}} MATHEMATICA Table[Length[Select[Subsets[Subsets[Range[n]]], MemberQ[#, {}]&&Union@@#==Range[n]&&SubsetQ[#, Intersection@@@Tuples[#, 2]]&]], {n, 0, 3}] CROSSREFS The case also closed under union is A000798. The connected case (i.e., with maximum) is A102894. The same for union instead of intersection is (also) A102894. The non-covering case is A102895. The BII-numbers of these set-systems (without the empty set) are A326880. The unlabeled case is A326883. Cf. A003465, A014466, A102896, A102897, A193674, A193675, A306445, A307249, A326878. Sequence in context: A193436 A193501 A133990 * A120808 A092204 A079874 Adjacent sequences:  A326878 A326879 A326880 * A326882 A326883 A326884 KEYWORD nonn,more AUTHOR Gus Wiseman, Jul 30 2019 EXTENSIONS a(5)-a(7) from Andrew Howroyd, Aug 10 2019 STATUS approved

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Last modified July 29 09:28 EDT 2021. Contains 346343 sequences. (Running on oeis4.)